1. Associative Hierarchical CRFs for Object Class Image Segmentation
International Conference on Computer Vision (ICCV) 2009
L’ubor Ladick’y and Chris Russell
Oxford Brookes University
Pushmeet Kohli
Microsoft Research Cambridge
Philip H.S. Torr
Oxford Brookes University

2. Outline Introduction Random Fields for Labelling Problems
Hierarchical CRF for Object Segmentation
Experiments and Results

3. Structure

4. Introduction

5. Distribution of identical billiard balls
Mean Shift
Region of
interest
Center of
mass
Mean Shift
vector
Objective : Find the densest region
Distribution of identical billiard balls

6. Distribution of identical billiard balls
Mean Shift
Region of
interest
Center of
mass
Mean Shift
vector
Objective : Find the densest region
Distribution of identical billiard balls

7. Distribution of identical billiard balls
Mean Shift
Region of
interest
Center of
mass
Mean Shift
vector
Objective : Find the densest region
Distribution of identical billiard balls

8. Distribution of identical billiard balls
Mean Shift
Region of
interest
Center of
mass
Mean Shift
vector
Objective : Find the densest region
Distribution of identical billiard balls

9. Distribution of identical billiard balls
Mean Shift
Region of
interest
Center of
mass
Mean Shift
vector
Objective : Find the densest region
Distribution of identical billiard balls

10. Distribution of identical billiard balls
Mean Shift
Region of
interest
Center of
mass
Mean Shift
vector
Objective : Find the densest region
Distribution of identical billiard balls

11. Distribution of identical billiard balls
Mean Shift
Region of
interest
Center of
mass
Objective : Find the densest region
Distribution of identical billiard balls

12. Pixel V.S. Segment Based on pixels: Based on segments
The difference of pair CRFs between based on pixels and segments
Based on pixels:
No quantization errors
Lack of long range interactions
Results oversmoothed
Based on segments
Allows long range interactions
Can not recover from incorrect segmentation

13. Introduction Propose a novel hierarchical CRF
Integration of features derived for different quantisation levels
Propose new sophisticated potentials defined over the different levels of the quantisation hierarchy
Use a novel formulation that allows context to be incorporate at multiple levels of multiple quantisation

14. Random Fields for Labelling Problems
Introduce the pixel-based CRF used for formulation the object class segmentation problem
One discrete R.V. per image pixel, each of which may take a value from the set of labels
Symbols:
Label:
R.V. :
Pixel
The set of all neighbours of the variable :
A clique c is a set of random variables
Labelling: denoted by take the value from

15. CRFs
D: the set of the data, Z: the partition function, C: the set of all cliques
: the potential function of the clique ,
The energy form:
The most probable or MAP labeling :
Wrote as the sum of unary and pairwise potentials

16. The Robust 𝑃 𝑁 Model
Extended by the robust 𝑃 𝑁 potentials [KohLi et al., 2008 ]
S: the set of the segments
The pixels within the same segment are more like likely to take the same label
the form of the robust 𝑃 𝑁 potentials: ;
The weighted version:

17. 𝑃 𝑁 -Based Hierarchical CRFs
The single auxiliary variable 𝑦 𝑐 where c is a segment or a clique
Take the value from an extended label set

18. 𝑃 𝑁 -Based Hierarchical CRFs
New cost function over
The unary potential over Y,
𝜓 𝑐 ( 𝑦 𝑐 )= 𝛾 𝑐 𝓁 , 𝑦 𝑐 ∈ℒ & 𝛾 𝑐 𝑚𝑎𝑥 , 𝑦 𝑐 = 𝐿 𝐹
The pairwise potential
over Y and X
𝜓 𝑐 ( 𝑦 𝑐 , 𝑥 𝑖 ) = 0 , 𝑦 𝑐 = 𝐿 𝐹 𝑜𝑟 𝑦 𝑐 = 𝑥 𝑖 & 𝑤 𝑖 𝑘 𝑐 𝑙 ,𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝑤ℎ𝑒𝑟𝑒 𝑙= 𝑥 𝑖
Goal:
The new energy function:
𝐸 𝒙 = 𝑖∈𝒗 𝜓 𝑖 ( 𝑥 𝑖 ) + 𝑖∈𝒗,𝑗∈ 𝑵 𝑖 𝜓 𝑖𝑗 ( 𝑥 𝑖 , 𝑥 𝑗 )
+min 𝑦 ( 𝑐∈𝑺 𝜓 𝑐 𝑝 𝑥, 𝑦 𝑐 + 𝑐,𝑑∈𝑺 𝜓 𝑐,𝑑 𝑦 𝑐 , 𝑦 𝑑 )

19. Recursive Form
The auxiliary variables in the last layer are the input variable
The new energy function:
𝐸 𝒙 = 𝑖∈𝒗 𝜓 𝑖 ( 𝑥 𝑖 ) + 𝑖∈𝒗,𝑗∈ 𝑵 𝑖 𝜓 𝑖𝑗 ( 𝑥 𝑖 , 𝑥 𝑗 ) +min 𝑦 ( 𝑐∈𝑺 𝜓 𝑐 𝑝 𝑥, 𝑦 𝑐 + 𝑐,𝑑∈𝑺 𝜓 𝑐,𝑑 𝑦 𝑐 , 𝑦 𝑑 )
The recursive form:
𝐸 𝑛 𝑥 𝑛−1 , 𝑥 𝑛 = 𝑐∈ 𝑆 (𝑛) 𝜓 𝑐 𝑝 ( 𝒙 𝑐 𝑛+1 , 𝑥 𝑐 𝑛 ) + 𝑐𝑑∈ 𝑁 (𝑛) 𝜓 𝑐𝑑 𝑥 𝑐 𝑛 , 𝑥 𝑑 𝑛 + min 𝑥 (𝑛+1) 𝐸 𝑛+1 ( 𝒙 𝑛 , 𝒙 𝑛+1 )
Initial form: 𝐸 0 𝒙 = 𝑖∈ 𝑆 (0) 𝜓 𝑖 ( 𝑥 𝑖 0 ) + 𝑖𝑗∈ 𝑁 (0) 𝜓 𝑖𝑗 𝑥 𝑖 𝑜 , 𝑥 𝑗 𝑜 + min 𝑥 (1) 𝐸 1 ( 𝒙 0 , 𝒙 1 )

20. Hierarchical CRF for Object Segmentation
Describe the set of potentials in the object-class segmentation problem
Include unary potentials for both pixels and segments, pairwise potentials between pixels and segments and connective potentials between pixels and their containing segments

21. Robustness to misleading segmentations
Using unsupervised segmentation algorithm may be misleading – segment may contain multiple object classed
Assigning the same label to all pixels will result in an incorrect labeling
Overcome it by using the segment quality measures [Rabinovich et at., 2009] and [Ren and Malik, 2003]
By modifying the potentials according to a quality sensitive measure for all segment c
Writing 𝜆 𝑐 : weight 𝜉 𝑐 : features based potential over c

22. Potentials for object class segmentation
Refer to elements of each layer as pixels, segments, and super- segments
At the pixel level:
The unary potentials are computed using a boosted dense feature classifier [Shotton et al., 2006]
The pairwise potentials [Boykov and Jolly, 2001] , [Rother at al., 2004]:

23. Potentials for object class segmentation
At the segment level:
Initially found using a fine scale mean-shift algorithm [Comaniciu and Meer, 2002]
Contain little novel local information, but strong predictors of consistency
The potentials learning at this level are uniform, due to the lack of unique features, however as they are strongly indicative of local consistency, the penalty associated with breaking them is high
To encourage neighbouring segments with similar texture to take the same label, used pairwise potentials based on the Euclidean distance if normalized histograms of colour

24. Potentials for object class segmentation
At the super-segment level:
Based upon a coarse mean-shift segmentation, performed over the result of the previous segmentations
Contain significantly more internal information than their smaller children
Propose unary segment potential based on the histograms of features

25. Unary Potentials From Dense Feature
Perform texture based segmentation at pixel level
Derived from TextonBoost [Shotton et al., 2006]
The features are computed on every pixel
Extend the TextonBoost by boosting classifiers defined on multiple dense feature together
Dense–feature shape filters defined by triplets: [f, t, r] where f is a feature type, t is a feature cluster, and r is a rectangular region
Feature response : Given a point i, the number of features of type f belong to the cluster t in the region r relative to the point i

26. Histogram-Based Segment Unary Potentials
Defined over segments and super-segments
The distribution of dense features responses are more discriminative than any feature along
The unary potential of an auxiliary variable representing a segment is learnt by (using the normalized histograms of multiple clustered dense features) using multi-class Gentle Ada-boost[Torralba et al., 2004]
Weak classifiers: f: the normalized histogram of the feature set t: the cluster index a: threshold

27. Histogram-Based Segment Unary Potentials
The segment potential: a : the response given by the Ada-boost classifier to clique c taking label l a : the truncation threshold a , and a normalizing constant

28. Learning Weights for Hierarchical CRFs
Uses a coarse to fine, layer-based, local search scheme over a validation set
Introduce additional notation:
: the variable contained in the layer
: the labelling of associated with a MAP estimate
Determine a dominant label for each segment c, such that when , if there is no such dominant label, set a ⟹ 𝐿 𝑐 = 𝑙 , 𝑖∈𝑙 Δ( 𝑥 𝑖 =𝑙)≥0.5 𝑐 & 𝐿 𝐹 , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
The label of a clique : correspond to the dominant label of this clique(segment) in the ground truth (or ) for its containing ot be correctly labelled

29. Learning Weights for Hierarchical CRFs
At each layer, seek to minimize the discrepancy between the dominant ground truth of a clique(segment), and the value of the MAP estimate
Choose parameters λ to minimize

30. Algorithm
: the weighting of unary terms in the layer a : the weighting of pairwise terms in the layer a : a scalar modifier of all terms in the layer a : an arbitrary constant that controls the precision of the final assignment of

31. Experiments Two data sets MSRC-21 [Shotton et al., 2006]
Resolution: 320×213 pixels
21 object classes
PASCAL VOC 2008 [Everingham et al., 2008, website]
511 training, 512 validation and 512 segmented test images
20 foreground and 1 background classes
10, 057 images for which only the bounding boxes of the objects present in the image are marked

32. Results on The MSRC-21

33. Results on The MSRC-21 [25]: J. Shotton et al., CVPR, 2008
[26]: J. Shotton et al., ECCV, 2006
[1]: D. Batra et al., CVPR, 2008
[25]: L. Yang et al., CVPR, 2007

34. Results on The MSRC-21 [25]: J. Shotton et al., CVPR, 2008
[26]: J. Shotton et al., ECCV, 2006
[1]: D. Batra et al., CVPR, 2008
[25]: L. Yang et al., CVPR, 2007

35. Results on The VOC-2008

36. Results on The VOC-2008